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Extremal Properties of the First Eigenvalueof Schrödinger-Type Operators

✍ Scribed by Lino Notarantonio

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
212 KB
Volume
156
Category
Article
ISSN
0022-1236

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✦ Synopsis

Given a separable, locally compact Hausdorff space X and a positive Radon measure m(dx) on it, we study the problem of finding the potential V(x) 0 that maximizes the first eigenvalue of the Schro dinger-type operator L+V(x); L is the generator of a local Dirichlet form (a, D[a]) on L 2 (X, m(dx)).

1998 Academic Press

(1) the supremum sup[* 1 (V): V # B A ] is finite;

(2) there exists V # B A such that sup[* 1 (V ): V # B A ]=* 1 (V ).

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